The approximating function \(f^\nu \)  in this subsection is closely related to augmented Lagrangians within the general duality framework of [1]}. This observation also points to the possibility of developing exact Rockafellians by replacing \(\iota _{\lbrace 0\rbrace ^m}(u)\)  with \(\theta \Vert u\Vert _1\)  in the definition of \(f\) . Via Proposition REF , this leads to exactness results parallel to that in Theorem REF , at least when each \(G_i\)  as well as \(f_0\)  are continuously differentiable and the “standard” qualification [2]} holds.
